Theorems · Theorem · general topology
TopologicalSpace.vietoris.continuous_range_of_finite
∀ {α : Type u_1} [inst : TopologicalSpace α] {ι : Type u_4} [Finite ι], Continuous Set.range- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.ofPredproof · cited by 6,101
- Set.rangestatement · cited by 4,705
- Finitestatement and proof · cited by 3,029
- Continuousstatement · cited by 2,592
- IsOpenproof · cited by 2,400
- IsClosedproof · cited by 1,639
- IsOpen.preimageproof · cited by 147
- IsClosed.preimageproof · cited by 138
- continuous_applyproof · cited by 120
- Set.ofPred_forallproof · cited by 48
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.vietoris.isPreconnected_nonempty_finite_subsetsproof · cited by 1